Patent Literature 1 discloses a surface-emitting laser element having a two-dimensional periodic structure. This surface-emitting laser element includes a photonic crystal layer. The photonic crystal layer disclosed in the same Literature has a structure in which holes are periodically provided in two orthogonal directions. Non-Patent Literature 1 discloses an example in which a phase shift region having a period different from that of the surrounding is inserted between hole forming regions. By using a phase shift region, a beam pattern different from that obtained without using a phase shift region can be obtained. Particularly, an annular beam is effective for optical tweezers. With a normal unimodal beam, it is difficult to capture an opaque substance, however, an annular beam can also be used to capture an opaque substance (Non-Patent Literature 2). Patent Literature 2 discloses a projector using a surface-emitting laser element. Generally, a projector is a device that forms a desired image by selectively transmitting/blocking light for each pixel, and does not control a phase of a wavefront for each pixel.
If it is possible to control phases of wavefronts of the respective micro areas of a two-dimensionally spreading laser beam, by overlapping wave fronts of the respective micro areas, a desired image can be obtained. Considering that a far-field image of a laser is obtained by Fourier-transforming a near field image of the two-dimensionally spreading laser beam, various applications of such a semiconductor laser device can be expected. It is known that a reproduced image can be obtained by applying Fourier transform to a hologram, and a device for this is expected to be also used for hologram designing, etc. A Fourier transform image is used for image processing in an inspection device and pattern matching, etc.